Editing Analysis of variance (section)

===Partitioning of the sum of squares===
{{main|Partition of sums of squares}}
[[File:Example ANOVA Table.png|thumb|324x324px|One-factor ANOVA table showing example output data]]
{{see also|Lack-of-fit sum of squares}}
ANOVA uses traditional standardized terminology. The definitional equation of sample variance is <math display="inline">s^2 = \frac{1}{n-1} \sum_i (y_i-\bar{y})^2</math>, where the divisor is called the degrees of freedom (DF), the summation is called 
the sum of squares (SS), the result is called the mean square (MS) and the squared terms are deviations from the sample mean. ANOVA estimates 3 sample variances: a total variance based on all the observation deviations from the grand mean, an error variance based on all the observation deviations from their appropriate treatment means, and a treatment variance. The treatment variance is based on the deviations of treatment means from the grand mean, the result being multiplied by the number of observations in each treatment to account for the difference between the variance of observations and the variance of means.

The fundamental technique is a partitioning of the total [[sum of squares (statistics)|sum of squares]] ''SS'' into components related to the effects used in the model. For example, the model for a simplified ANOVA with one type of treatment at different levels.

<math display="block">SS_\text{Total} = SS_\text{Error} + SS_\text{Treatments}</math>

The number of [[Degrees of freedom (statistics)|degrees of freedom]] ''DF'' can be partitioned in a similar way: one of these components (that for error) specifies a [[chi-squared distribution]] which describes the associated sum of squares, while the same is true for "treatments" if there is no treatment effect.

<math display="block">DF_\text{Total} = DF_\text{Error} + DF_\text{Treatments}</math>